Calculate the Area of a Square: ABCD Vertex Problem

Q: How do I know the side length is 10/x from the diagram?

Look at the diagram labels carefully! The side is marked as $ \frac{10}{x} $, which means 10 divided by x. This algebraic expression represents the length of each side of the square.

Q: Why do I square the fraction instead of just the top number?

Because area = side × side, and when you multiply fractions, you multiply numerators together and denominators together: $ \frac{10}{x} \times \frac{10}{x} = \frac{10 \times 10}{x \times x} = \frac{100}{x^2} $

Q: What does x represent in this problem?

x is a variable that could represent any positive number. The side length changes as x changes - when x is bigger, the side $ \frac{10}{x} $ gets smaller!

Q: Can I simplify the answer 100/x² further?

No, $ \frac{100}{x^2} $ is already in its simplest form. Since 100 and $ x^2 $ don't share common factors (we don't know what x is), this fraction cannot be reduced.

Q: How do I check if my area formula is correct?

Substitute a test value for x! If x = 5, then side = $ \frac{10}{5} = 2 $, so area = $ 2^2 = 4 $. Using your formula: $ \frac{100}{5^2} = \frac{100}{25} = 4 $ ✓

Square Area Formula with Algebraic Side Lengths

Look at the square below:

Which expression represents its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the area of the square

00:03 Side length according to the given data

00:07 We'll use the formula for calculating the area of a square (side squared)

00:15 We'll substitute appropriate values and solve to find the area

00:23 Make sure to square both numerator and denominator

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the square below:

Which expression represents its area?

Step-by-step solution

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=\frac{10^2}{x^2}=\frac{100}{x^2}$

Final Answer

$\frac{100}{x^2}$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Square area equals side length squared: $A = s^2$
Technique: Side length $\frac{10}{x}$ gives area $\left(\frac{10}{x}\right)^2 = \frac{100}{x^2}$
Check: Verify by substituting values: when x=2, side=5, area=25 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square the entire fractional side length
Don't just square the numerator = $\frac{10^2}{x} = \frac{100}{x}$ ! This ignores the denominator and gives the wrong formula. Always square both numerator and denominator: $\left(\frac{10}{x}\right)^2 = \frac{10^2}{x^2} = \frac{100}{x^2}$ .

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

How do I know the side length is 10/x from the diagram?

Look at the diagram labels carefully! The side is marked as $\frac{10}{x}$ , which means 10 divided by x. This algebraic expression represents the length of each side of the square.

Why do I square the fraction instead of just the top number?

Because area = side × side, and when you multiply fractions, you multiply numerators together and denominators together: $\frac{10}{x} \times \frac{10}{x} = \frac{10 \times 10}{x \times x} = \frac{100}{x^2}$

What does x represent in this problem?

x is a variable that could represent any positive number. The side length changes as x changes - when x is bigger, the side $\frac{10}{x}$ gets smaller!

Can I simplify the answer 100/x² further?

No, $\frac{100}{x^2}$ is already in its simplest form. Since 100 and $x^2$ don't share common factors (we don't know what x is), this fraction cannot be reduced.

How do I check if my area formula is correct?

Substitute a test value for x! If x = 5, then side = $\frac{10}{5} = 2$ , so area = $2^2 = 4$ . Using your formula: $\frac{100}{5^2} = \frac{100}{25} = 4$ ✓

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Calculate the Area of a Square: ABCD Vertex Problem

Square Area Formula with Algebraic Side Lengths

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know the side length is 10/x from the diagram?

Why do I square the fraction instead of just the top number?

What does x represent in this problem?

Can I simplify the answer 100/x² further?

How do I check if my area formula is correct?

🌟 Unlock Your Math Potential

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